# Calculus (Antiderivatives)

What is the antiderivative of the following expression?
3x(x^2 + 7)^3

1. hard way: expand the product:
3x^7 + 63x^5 + 441x^3 + 1029x
integral is
3/8 x^8 + 21/2 x^6 + 441/4 x^4 + 1029/2 x^2

easy way: let u = x^2+7
du = 2x dx
Integral of 3/2 u^3 du
is
3/8 u^4 = 3/8 (x^2+7)^4

posted by Steve

## Similar Questions

1. ### Calculus (Antiderivatives)

What is the antiderivative of the followring expression? x^(-1/2) sin(2x^(-3/2)) After trying to figure out this problem, I have the suspicion that the antiderivative cannot be found using substition method, would this assumption
2. ### derivative am i right or wrong

what is the antiderivative of 1/(x^2-2x+2)? does antiderivative mean find the derivative of the function or integrate it. is the answer ln(x^2-2x+2) or is-2(x^2-2x+2)^-2. These are part of the multiple choices. antiderivative is
3. ### math

Consider the function f(t)=2sec^2(t)–6t^2 . Let F(t) be the antiderivative of f(t) with F(0)=0 . Then F(5)=? I am confused on how I would find the antiderivative, after I do that do I plug in five?
4. ### Math

Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative. Remember to use ln |u| where appropriate.) (x^5+x^3+8x)/x^4
5. ### Calculus

What is the antiderivative of this? What is the antiderivative of x/((16+x^2)^(1/2))? (x / the square root of (16 + x^2))? What method did you use? Substitution, etc..? Thanks!

The indefinite integral, or which call the "antiderivative", of f'(x)=6x-8x^3 is f(x) = 3x^2 - 2x^4 + C where C is any constant. Plug in x = 2 to that to see what C is. 3 = 3*4 - 2*16 + C Determine the antiderivative of the
7. ### calculus - antiderivative

can someone help me find the antiderivative of: f'(x) = (x^2-1)/x where f(1)=1/2, and f(-1) = 0 Thanks!
8. ### math

what would the antiderivative of e^-2x be? and if the antiderivative of that is -1/2e^-2x, what would that antiderivative be?
9. ### AP Calculus BC

Hi! Thank you very much for your help--- I'm not sure what the answer to this is; how do I solve? Find antiderivative of (1/(x^2))[sec(1/x)][tan(1/x)]dx I did integration by parts and got to (1/(x^2))[sec(1/x)] + 2*[antiderivative
10. ### Calculus (Antiderivatives)

Suppose f(x) is a continuous function. Then a function F(x) such that F'(x) = f(x) is called: A.) the indefinite integral of f B.) the antiderivative of f C.) an antiderivative of f D.) a definite integral of f E.) All of the

More Similar Questions